Labeled-Particle Hybrid Monte Carlo–Discrete Ordinates Transport with Quasi–Monte Carlo Sampling

We present a hybrid Monte Carlo (MC)–discrete ordinates method for linear transport based on a labeled-particle decomposition. The method combines explicit-scattering MC, hybridized MC, and a deterministic SN clean-up solve. In explicit mode, scattering is sampled directly; in hybridized mode, particles stream without sampled scattering, and the removed scattering contribution is accumulated as a deterministic source. We focus on a scatter history–based switching rule in which particles transfer to hybridized mode after Ns collisions and also demonstrate several alternative handoff policies. Relabeling from the deterministic representation back to particle form reconstructs the particle population while preserving source accounting, which allows the work split to be reset from step to step and supports quasi–Monte Carlo (QMC) sampling on fixed-dimensional source variables. Numerical results on steady and transient benchmarks show that finite-Ns hybrids can improve the effectiveness of source-sampled QMC while providing a practical lever for redistributing work between the particle and deterministic stages. The resulting framework opens a broad policy design space for balancing accuracy, cost, and implementation priorities.